Like you, I was unaware of this parameter.
NB: in the case of sufficient comprehensive treatment, the oxygen captured by the oxidation of nitrogen is recovered during the denitrification phase. You have to take it into account; otherwise you risk distorting your oxygenation needs.
Who is this author?
The 4.5 factor corresponds to the amount of O2 required for ammonification and nitrification. As explained previously, this formula only takes into account the O2 requirements—the contribution from denitrification is not incorporated into this parameter. What surprises me the most is that the amount of COD is not altered by a coefficient, which means that for 1 kg oxidized COD, you consume 1 kg of O2. Usually, a coefficient of 0.7 is applied to COD (maybe there are more precise figures for agricultural effluent).
I wonder if this equation doesn't apply to solid rather than liquid waste (example O2 needed for composting). This would explain on the one hand the lack of a COD coefficient and on the other the fact that the contribution of O2 from denitrification is not taken into account.